Related papers: Codes for error detection, good or not good
The mds (maximum distance separable) conjecture claims that a nontrivial linear mds $[n,k]$ code over the finite field $GF(q)$ satisfies $n \leq (q + 1)$, except when $q$ is even and $k = 3$ or $k = q- 1$ in which case it satisfies $n \leq…
LCD BCH codes are an important class of cyclic codes which have efficient encoding and decoding algorithms, but their parameters are difficult to determine. The objective of this paper is to study the LCD BCH codes of length…
We consider the problem of constructing a code capable of correcting a single long tandem duplication error of variable length. As the main contribution of this paper, we present a $q$-ary efficiently encodable code of length $n+1$ and…
This paper improves the antiGriesmer bound for linear anticodes previously established by Chen and Xie (Journal of Algebra, 673 (2025) 304-320). While the original bound required the code length to satisfy $n < q^{k-1}$ and the dual code to…
Construction of error-correcting codes achieving a designated minimum distance parameter is a central problem in coding theory. In this work, we study a very simple construction of binary linear codes that correct a given number of errors…
A q-query locally testable code (LTC) is an error correcting code that can be tested by a randomized algorithm that reads at most q symbols from the given word. An important question is whether there exist LTCs that have the ccc-property:…
The capacity of symmetric instance of the multiple unicast index coding problem with neighboring antidotes (side-information) with number of messages equal to the number of receivers was given by Maleki, Cadambe and Jafar. In this paper we…
The weighted-Hamming metric generalizes the Hamming metric by assigning different weights to blocks of coordinates. It is well-suited for applications such as coding over independent parallel channels, each of which has a different level of…
Locally recoverable (LRC) codes provide a solution to single node failure in distributed storage systems, where it is a very common problem. On the other hand, linear complementary dual (LCD) codes are useful in fault injections attacks on…
For a number of quantum channels of interest, phase-flip errors occur far more frequently than bit-flip errors. When transmitting across these asymmetric channels, the decoding error rate can be reduced by tailoring the code used to the…
A quantum error correcting code is a subspace $\mathcal{C}$ such that allowed errors acting on any state in $\mathcal{C}$ can be corrected. A quantum code for which state recovery is only required up to a logical rotation within…
The minimum distance of a code is an important concept in information theory. Hence, computing the minimum distance of a code with a minimum computational cost is a crucial process to many problems in this area. In this paper, we present…
A linear code with parameters $[n, k, n-k+1]$ is called a maximum distance separable (MDS for short) code. A linear code with parameters $[n, k, n-k]$ is said to be almost maximum distance separable (AMDS for short). A linear code is said…
Linear error-correcting codes form the mathematical backbone of modern digital communication and storage systems, but identifying champion linear codes (linear codes achieving or exceeding the best known minimum Hamming distance) remains…
Cyclic codes are a subclass of linear codes and have applications in consumer electronics, data storage systems, and communication systems as they have efficient encoding and decoding algorithms. Let $m=2\ell+1$ for an integer $\ell\geq 1$…
We present lower bounds on the minimum pseudocodeword effective Euclidean distance (or minimum "pseudodistance") for coded modulation systems using linear codes with $q$-ary phase-shift keying (PSK) modulation over the additive white…
We provide bounds for codes for a non-symmetric channel or, equivalently, for ternary codes with the Manhattan distance.
Performance analysis of optimal signal detection using quantized received signals of a linear vector channel, which is an extension of code-division multiple-access (CDMA) or multiple-input multiple-output (MIMO) channels, in the large…
The problem of error control in random linear network coding is addressed from a matrix perspective that is closely related to the subspace perspective of K\"otter and Kschischang. A large class of constant-dimension subspace codes is…
In this paper, we give a method for constructing linear codes with small hulls by generalizing the method in \cite{LCD-T-matric}. As a result, we obtain many optimal Euclidean LCD codes and Hermitian LCD codes, which improve the previously…